They don't need to have enemies like zombies or wild animals, but I'm not against that either. I prefer ones that seem kind of like a simulation (meaning you have to eat, drink and maybe sleep to survive). I've played WarZ and loved it, but I don't very much like the mmo part. I mainly enjoyed that loot/equip system where they are specific slots for items or ones where you have to rearrange items in your bag to make them fit. It reminded me of RPG games I played as a kid and made it feel more "real" so to speak. Graphics are not a big issue with me, but I would prefer them to be decent enough (NOT Fallout 1 and 2 graphics). The one's I've played that I can think of are listed below, so refrain from posting those. Thank you in advance.
The full Fallout series since one
Infestation Survivor Stories (The WarZ)
7 Days to Die
All of the Elder Scrolls since Daggerfall
Farcry trilogy
Minecraft
Miasmata
Fallen Earth
Arma 3 (if you could count that)
That's all I can think of for now.
Added (1). Another thing, it doesn't have to have a story. I'm fine with being thrown into a world and told to just survive.
Added (2). I should also add, co-op is always good. Meaning, I can invite someone to join my server or my game privately without the worry of it being filled to the brim with griefers.